Three-man chess boards are known which allow temporary participation of three instead of two parties. One of these is disclosed in the newspaper "Die Zeit" No. 15 of Apr. 6, 1973, page 71. Another is disclosed in the magazine "Stern" No. 46 of November, 1973, page 93.
If, in the above games, the king of one party is checkmated, this party is eliminated and the game becomes a game for two parties. This creates a disturbing change in the game and an unbalanced situation, as the remaining chess-men of the eliminated party can be used by the checkmating party or remain on the field as unmoving obstacles, or are moved from the board altogether.
In one of the known games, the positioning of the square and oblique angled quadrangles causes a transition problem from the starting point of the one party to the starting point of the other. Those must be eliminated with transit fields and additional rules for moves which are valid only in these transit fields.
The other known game avoids transit fields. However, as six oblique angles quadrangles collide in the center of the board, the homogeneity of the rules of movement is interrupted.
If one defines the "degree of freedom Fr." of movement of a chessman as a relation between the number of possible moves L and the number of parties S, then the queen in the two-man chess game represents a value Fr. = L/S = 4/2 = 2 and the queen of the previously mentioned three-man chess game has a value of: Fr. = L/S = 4/3 = 1.33. The degree of freedom of all of the chess men of these games is thus lower by 1/3. Therefore the situation for one party, who is being pressed by the other two participants, soon becomes hopeless, as his chess men find no protection and as there are no additional escape facilities on the normal squares.
There are also three-man chess boards with triangular fields (German Patents Nos. 14484 and 24253), one of which divides the squares into two triangular fields and consequently does not allow the positioning of both parties with equal chances. In the other game with fields of equilateral triangles, which positions eight chess men in one row, the geometry of the fields causes an asymmetrical starting position for the chess men and uneven starting chances for corresponding chess men such as, e.g., the right and left castles.